The tree stump is approximately 2.64 feet tall. This is solved using the Tangent Function.
What is the explanation for the above response?Let's assume that the height of the tree stump is h feet.
Since the roots of the tree extend out from the base of the tree the same distance that the stump is tall, the distance between the end of the roots and the top of the stump is also h feet.
Therefore, the total distance covered by the 2x4's is 2h feet (h feet up to the top of the stump and h feet down to the end of the roots).
We can use the tangent function to find the angle of incline. The tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the opposite side is h and the adjacent side is 5 feet. So, we have:
tan θ = h/5
To maximize the angle of incline, we want to maximize the value of θ. This occurs when tan θ is as large as possible.
Since the tangent function is an increasing function, we can find the largest possible value of tan θ by finding the largest possible value of h.
Solving for h in the equation tan θ = h/5, we get:
h = 5 tan θ
Since the length of the boards is 5 feet, we know that:
2h = 5
Substituting for h, we get:
2(5 tan θ) = 5
10 tan θ = 5
tan θ = 0.5
Using a calculator or a table of tangent values, we can find that the angle whose tangent is 0.5 is approximately 26.57 degrees.
Therefore, the height of the tree stump is:
h = 5 tan θ
h = 5 tan 26.57
h ≈ 2.64 feet
So, the tree stump is approximately 2.64 feet tall.
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(3) Two cylinder of equal volume have
heights in the ratio 1:16. Find the
ratio of their radii.
The ratio between their radii of cylinder is therefore 1:4.
WHAT IS RADIUS?The distance between a circle's or sphere's centre and its edge is referred to in geometry as its radius1. It is known as "r" and is a crucial component of spheres and circles3.
For instance, if a circle has a radius of 5 cm, that indicates that the circle's center to edge distance is 5 cm3.
When two cylinders have 1:16 ratios for their volumes and heights, it is possible to calculate their radii as follows:
Assume that one cylinder has a radius of r and a height of h. The other cylinder will have a radius of R and a height of 16h.
As the volumes of both cylinders are equal, we may write:
πr²h = πR²(16h) (16h)
r²/R² = 1/16
r/R = √(1/16) = 1/4
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358 words typed in 5 minutes
Fraction is a part of whole.Fractions are written in the form of two numbers, one on top of the other, separated by a horizontal line. The number on the top is called the numerator, and the number at the bottom is called the denominator.
What is fraction?
A fraction is a mathematical concept that represents a part of a whole or a group. It is a way of expressing a number that is less than one and greater than zero.
The numerator represents the part of the whole or group that is being referred to, and the denominator represents the total number of parts in the whole or group. For example, if we have a pizza that is cut into eight equal slices, and we eat three slices, we can represent the amount of pizza we ate as the fraction 3/8. In this case, the numerator is 3, which represents the number of slices we ate, and the denominator is 8, which represents the total number of slices in the pizza.
Fractions can be used in a variety of mathematical operations, including addition, subtraction, multiplication, and division. To add or subtract fractions, the denominators must be the same. If they are not, the fractions must be converted into equivalent fractions with the same denominator before they can be added or subtracted.
Multiplying fractions involves multiplying the numerators together and the denominators together. Dividing fractions involves multiplying the first fraction by the reciprocal of the second fraction, which is obtained by switching the numerator and denominator of the second fraction.
Fractions are commonly used in everyday life, such as when cooking or measuring ingredients, calculating percentages, and dealing with money. For example, if a store is having a sale with a discount of 20%, we can represent the sale price as the fraction 4/5, since the price after the discount is 80% of the original price.
It is important to note that fractions can also be expressed as decimals or percentages. To convert a fraction to a decimal, we divide the numerator by the denominator. To convert a fraction to a percentage, we multiply the fraction by 100.
In conclusion, fractions are an important concept in mathematics and are used in many different areas of our daily lives. They represent a part of a whole or group and are written in the form of a numerator over a denominator. Fractions can be used in a variety of mathematical operations and can be expressed as decimals or percentages.
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Correct question is "What is fraction? Write 358 words about it "
5x^2-15x-50 factor the polynomial
Answer:
5(x - 5)(x + 2)
Step-by-step explanation:
5x² - 15x - 50
5(x² - 3x - 10)
5(x - 5)(x + 2)
please help rewarding brainliest
Answer: f(x)
Step-by-step explanation: It goes from the lowest elevation to the highest.
Chen subtracted two polynomials as shown. Explain Chen’s error.
P^2+7mp+4-(-2p^2-mp+1)
P^2+2p^2+7mp-mp+4+1
3p^2+6m+5
The correct answer is 3p² + 8mp + 3, which is different from Chen's answer of 3p² + 6m + 5.
What is a polynomial?
In mathematics, a polynomial is an expression consisting of variables (also known as indeterminates) and coefficients, which involves only the operations of addition, subtraction, and multiplication. Polynomials can have one or more terms, and each term can have one or more variables with non-negative integer exponents.
Chen's error is in the second line where they added the terms -(-2p²-mp+1) without distributing the negative sign to each term inside the bracket. The correct way to subtract a polynomial is to change the sign of each term inside the bracket and then add them to the other polynomial. So, the correct simplification would be:
P²+7mp+4-(-2p²-mp+1)
= P²+7mp+4+2p²+mp-1 (Distributing the negative sign)
= 3p²+8mp+3
Therefore, the correct answer is 3p² + 8mp + 3, which is different from Chen's answer of 3p² + 6m + 5.
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A solid metal sphere of radius 9 is melted and transformed into three identical spheres. What is the ratio of the surface area of one of these spheres to the surface area of the original sphere?
Ratio of surface area of one of the new spheres to surface area of original sphere is [tex]$\frac{1}{3}\sqrt[3]{3}$[/tex] when a solid metal sphere of radius 9 is melted and transformed into three identical spheres.
How to calculate the ratio of the surface area of one of these spheres to the surface area of the original sphere?
The original sphere has radius 9, so its surface area is:
[tex]$A_1 = 4\pi(9^2) = 324\pi$[/tex]
When the sphere is melted down and formed into three identical spheres, each sphere will have one-third of the original mass and one-third of the original volume. Since the spheres are identical, they will each have the same radius.
Let r be the radius of one of the new spheres. Then the volume of each new sphere is:
[tex]$V_2 = \frac{4}{3}\pi(r^3)$[/tex]
Since the original sphere has been split into three identical spheres, the total volume is:
[tex]$V_{total} = 3(\frac{4}{3}\pi(r^3)) = 4\pi(r^3)$[/tex]
Since the original sphere and the three new spheres have the same total volume, we can set their volumes equal to each other:
[tex]$4\pi(9^3) = 4\pi(r^3)$[/tex]
Simplifying, we get:
[tex]$r = \frac{9}{\sqrt[3]{3}}$[/tex]
Now we can find the surface area of one of the new spheres:
[tex]$A_2 = 4\pi(r^2) = 4\pi(\frac{9}{\sqrt[3]{3}})^2 = \frac{108\pi}{\sqrt[3]{3}}$[/tex]
Finally, we can find the ratio of the surface area of one of the new spheres to the surface area of the original sphere:
[tex]$\frac{A_2}{A_1} = \frac{\frac{108\pi}{\sqrt[3]{3}}}{324\pi} = \frac{1}{3}\sqrt[3]{3}$[/tex]
Therefore, the ratio of the surface area of one of the new spheres to the surface area of the original sphere is [tex]$\frac{1}{3}\sqrt[3]{3}$[/tex].
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The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru is able to estimate their wait time more consistently and why?
Burger Quick, because it has a smaller IQR
Burger Quick, because it has a smaller range
Super Fast Food, because it has a smaller IQR
Super Fast Food, because it has a smaller range
The drive-thru is able tο estimate their wait time mοre cοnsistently will be A. Burger Quick, because it has a smaller IQR.
Hοw tο explain the IQR?The range οf values in the middle οf the scοres is knοwn as the interquartile range, οr IQR. The apprοpriate measure οf variability is the interquartile range when a distributiοn is skewed and the median is used instead οf the mean tο shοw a central tendency.
The cοrrect οptiοn here is Burger Quick, because it has a smaller IQR (Interquartile Range). IQR is the difference between the third quartile and the first quartile, which is represented by the bοx in the bοx plοt. In this case, the IQR fοr Burger Quick is 24 - 9.5 = 14.5, while the IQR fοr Super Fast Fοοd is 15.5 - 8.5 = 7. A smaller IQR indicates that the data is mοre cοnsistent and less spread οut.
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find the surface area of the composite figure/ triangular prism 10, 5, 10 height of 8cm/ rectangular prism 4, 5, 12, 4
Answer:
Therefore, the surface area of the composite figure is 368 cm².
Step-by-step explanation:
To find the surface area of the composite figure, we need to find the areas of each individual face and add them together.
The triangular prism has two triangular faces and three rectangular faces.
The area of each triangular face is 1/2(base × height).
Area of each triangular face = 1/2(10 × 5) = 25 cm²
The area of each rectangular face is length × width.
Area of the rectangular face with dimensions 5 cm by 10 cm = 5 × 10 = 50 cm²
Area of the rectangular face with dimensions 5 cm by 10 cm = 5 × 10 = 50 cm²
Area of the rectangular face with dimensions 10 cm by 8 cm = 10 × 8 = 80 cm²
Total area of the triangular prism = 2 × 25 + 3 × 50 + 80 = 280 cm²
The rectangular prism has two rectangular faces and four square faces.
The area of each rectangular face is length × width.
Area of the rectangular face with dimensions 4 cm by 5 cm = 4 × 5 = 20 cm²
Area of the rectangular face with dimensions 4 cm by 5 cm = 4 × 5 = 20 cm²
The area of each square face is side × side.
Area of each square face with side length 4 cm = 4 × 4 = 16 cm²
Total area of the rectangular prism = 2 × 20 + 4 × 16 = 88 cm²
The total surface area of the composite figure is the sum of the surface areas of the triangular prism and the rectangular prism.
Total surface area = surface area of triangular prism + surface area of rectangular prism
= 280 cm² + 88 cm²
= 368 cm²
in a term 1 maths test , whitney scored 55 marks and amir scored 40 marks in a term 2 maths test whitney increased her score by 2o percent and amir increased jis score by 20 marka who had the higher mark in term 2
Answer:
whitney
Step-by-step explanation:
so amir in term 2 has 40+20=60
and whitney has 55+11=66
11 because 20% of 55 is 11 and when you add that two numbers you got the answer that whitney have higher mark
10% of 55=5.5
20% = 10%×2
5.5×2=11
4-23 use the data in problem 4-22 and develop a regression model to predict selling price based on the square footage and number of bedrooms. use this to predict the selling price of a 2,000-square-foot house with three bedrooms. compare this model with the models in problem 4-22. should the number of bedrooms be included in the model? why or why not?
A regression model can be created to predict selling price based on square footage and number of bedrooms using available data. The model equation includes coefficients that can be estimated to predict the selling price of a house. The number of bedrooms is a significant predictor of selling price and should be included in the model.
To develop the regression model to predict selling price based on the square footage and number of bedrooms, the following steps can be taken:
Collect data on the selling price, square footage, and number of bedrooms for a sample of houses.
Create a scatter plot to visually inspect the relationship between selling price and square footage, and between selling price and number of bedrooms.
Use regression analysis to create a model that predicts selling price based on square footage and number of bedrooms. The model equation will be:
Selling price = b0 + b1(Square footage) + b2(Number of bedrooms)
where b0, b1, and b2 are coefficients to be estimated from the data.
To predict the selling price of a 2,000-square-foot house with three bedrooms, substitute the values into the model equation and solve for selling price:
Selling price = b0 + b1(2000) + b2(3)
Comparing the performance of this model with the models in problem 4-22. The number of bedrooms should be included in the model because it is a significant predictor of selling price. However, further analysis could be conducted to determine if other variables could improve the model's predictive power.
Overall, this regression model can provide a useful estimate of the selling price of a house based on its square footage and number of bedrooms.
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if a typist is able to type 5 pages in 10 minutes, then by your calculations, how many hours will it take the typist to type 60 pages?
Answer:
2 hours
Step-by-step explanation:
[tex]\frac{5}{10}[/tex] = [tex]\frac{60}{x}[/tex] Cross multiply and solve for x
5x = 600 Divide both sides by 5
x = 120
This is 120 minutes. 120 minutes is equal to 2 hours.
Helping in the name of Jesus.
Answer:
2 hours
Step-by-step explanation:
If 5 pages in 10 minutes and 60 pages than 60/5, which is 12. 12*10=120 minutes. 120 minutes is equivalent to 2 hours.
I need to know the steps too I’ve been struggling with this all week:/
Answer:
The answer would be 28.96
Step-by-step explanation:
Sorry I was'nt to explain step by step But I know the answer
Find the shaded area. Round your answer to the nearest tenth, if necessary.
Area of of the Triangle =
Area of the whole Rectangle =
Total Shaded Area =
Answer: For the triangle area you do= base*height what gives you 198in
For the rectangle area you do= side*lenght what gives you 756in
An for the shaded area you do triangle area-rectangle area, what gives you 558 in
Write the equation for a quadratic function that has x-intercepts of (-2,0) and (7,0) and passes through the point (5,-42).
The quadratic equation for a function having the x-intercepts of (-2,0) and (7,0) and passing through the point (5,-42) is:
f(x) = -2(x - 7)(x + 2)
The quadratic function has x-intercepts of (-2,0) and (7,0).
The function passes through the point (5,-42).Let's try to find the quadratic equation using the above information:
Since the quadratic function has x-intercepts of (-2,0) and (7,0), the function can be written as:
f(x) = a(x + 2)(x - 7)
Since the quadratic function passes through the point (5,-42), we can substitute the x and y coordinates into the above
equation to get the value of 'a':-
42 = a(5 + 2)(5 - 7)-42 = a(7)(-2)-42 = -14a => a = 3
So, the quadratic equation for the given function is:
f(x) = 3(x + 2)(x - 7)
Simplifying the equation:
f(x) = 3(x² - 5x - 14)f(x) = 3x² - 15x - 42
Therefore, the quadratic equation for a function having the x-intercepts of (-2,0) and (7,0) and passing through the point
(5,-42) is: f(x) = -2(x - 7)(x + 2)
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Use Figure 1 to answer the following question
Name a set of collinear points
Name a set of parallel lines
Name a set of concurrent lines
Name a ray
Name an obtuse angle
Name a right angle
Name a pair of adjacent angles
Name a pair of complementary angles
Name a pair of supplementary angles
Name a pair of vertical angles
The set of points and lines when named are listed below
Naming the set of points and linesUsing the figure as a guide, we have the following:
Name a set of collinear points: B and EName a set of parallel lines: AO and BEName a set of concurrent lines: SM and HNName a ray: OWName an obtuse angle: JBTName a right angle: BECName a pair of adjacent angles: BEC and BENName a pair of complementary angles: AOW and WOPName a pair of supplementary angles: AOB and WOPName a pair of vertical angles: TBG and PBERead more about points and lines at
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a quality control specialist at a plate glass factory must estimate the mean clarity rating of a new batch of glass sheets being produced using a sample of 18 sheets of glass. the actual distribution of this batch is unknown, but preliminary investigations show that a normal approximation is reasonable. the specialist should use a: group of answer choices t-distribution none of the distributions listed. z-distribution chi-square distribution f distribution
The quality control specialist should use a t-distribution for estimating the mean clarity rating of the new batch of glass sheets being produced using a sample of 18 sheets of glass.
The quality control specialist at a plate glass factory must estimate the mean clarity rating of a new batch of glass sheets being produced using a sample of 18 sheets of glass.
Since the actual distribution of this batch is unknown, but preliminary investigations show that a normal approximation is reasonable, the specialist should use a t-distribution.
1. The sample size (n) is 18, which is relatively small.
2. The population standard deviation (σ) is unknown.
In such cases, the t-distribution is more appropriate than the z-distribution, chi-square distribution, or f distribution.
The t-distribution is a statistical distribution that is used when the sample size is small, and the population standard deviation is unknown.
The z-distribution is used when the population standard deviation is known, and the sample size is large enough (typically, n > 30).
The chi-square distribution is used for testing the goodness-of-fit of a distribution or for testing the independence between two categorical variables.
The f distribution is used for comparing the variances of two populations.
It is not suitable for estimating the mean clarity rating in this case.
In conclusion, the quality control specialist should use a t-distribution for estimating the mean clarity rating of the new batch of glass sheets being produced using a sample of 18 sheets of glass.
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which statement about bar charts is true? group of answer choices bar charts are typically used to illustrate the pieces within a whole. bar charts cannot be used to compare amounts or quantities. bar charts are more versatile than pie charts and line charts. bar charts can be used to represent only a few types of data.
The statement "bar charts are more versatile than pie charts and line charts" is true.
The statement "bar charts are more versatile than pie charts and line charts" is true. Bar charts are versatile and can be used to compare data, show trends over time, and compare different categories or groups. They are especially useful for showing data with distinct categories, such as nominal data. In contrast, pie charts are limited in their use because they can only represent parts of a whole, while line charts are best suited for showing trends over time. Bar charts can be customized to display a wide range of information and are a valuable tool for communicating data effectively in a variety of contexts.
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The graph showing the total number of prisoners in state and federal prisons for the years 1960 through 2009 is shown in the figure. There were 204,608 prisoners in
1960 and 1,610,540 in 2009.
(1960,204608) and (2009,1610540)
Write the equation of the secant line joining these two points on the curve?
The Average rate of growth is 28589 per year
The Slope of the line connecting is m = 28589 pee year.
How to calculate the valueThe average rate of growth is a measure of how much a quantity or variable changes on average over a certain period of time. It is calculated by dividing the total change in the quantity by the length of the time period. The formula for the average rate of growth is:
Average Rate of Growth = (Final Value - Initial Value) / Time Interval
Average rate of growth = 1611,589-210733 / 2009-1960
= 28589 per year
Slope of the line connecting ( 1960, 210, 733) 4 (2009, 1,611, 589) will be:
m = У2 - y1 / x2 - x1
m = 28589 per year
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using gradient=rise/run find the gradient of ab in the following (0,6) and (3,2)
The gradient of the line segment AB is -4/3.
What is the gradient?
The gradient is a measure of the steepness of a curve or surface at a particular point. It is a vector quantity that points in the direction of the greatest increase in the function value and whose magnitude gives the rate of change of the function in that direction.
The coordinates of point A are (0, 6), and the coordinates of point B are (3, 2). We can find the gradient of the line connecting these two points using the formula:
gradient = rise/run
where "rise" is the difference in the y-coordinates of the two points, and "run" is the difference in the x-coordinates.
So, we have:
rise = 2 - 6 = -4
run = 3 - 0 = 3
Plugging these values into the formula, we get:
gradient = -4 / 3
Therefore, the gradient of the line segment AB is -4/3.
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PLEASE ANSWER!!!!!
Weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of $50. Find the probability that a worker selected at random makes between $400 and $550
Answer:
49.87%
Step-by-step explanation:
We know the following information:
$400 is the average weekly wage
$50 is the standard deviation (from the average wage)
To solve for the probability that a randomly-selected worker makes between $400-550, we have to solve for the standard score of each end of the range.
First, the standard score (Z) of $400:
[tex]Z = \dfrac{\text{value}-\text{average}}{\text{std deviation}}[/tex]
[tex]Z_{400} = \dfrac{400-400}{50} = 0[/tex]
The standard score of $400 is 0, since it is the average (mean) wage.
Second, the standard score of $550:
[tex]Z_{550} = \dfrac{550-400}{50} = 3[/tex]
The standard score of $550 is 3.
The probability that a worker's weekly wage is between $400 and $550 is equal to the probability that the standard score is between 0 and 3.
So, we can plug the standard scores that we just solved for into a distribution calculator to determine both probabilities.
P(0 < Z < 3) ≈ 49.87%
17. A circular track is represented by the equation x² - 18x + y²-22x = -177.
What is the center of the circular track?
A (3, 11)
B (6,9)
C (9,11)
D (3,9)
The answer is C) (9, 11) which represents the center of the circular track.
What is circle?A circle is a closed, two-dimensional shape where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the middle.
To find the center of the circular track, we need to convert the given equation into the standard form of the equation of a circle, which is:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius.
First, we need to complete the square for x and y terms:
x² - 18x + y² - 22x = -177
(x² - 18x + 81) + (y² - 22x + 121) = -177 + 81 + 121
(x - 9)² + (y - 11)² = 25
Now, we can see that the equation is in the standard form of the equation of a circle, where the center is (9, 11) and the radius is √25 = 5.
Therefore, the answer is C) (9, 11) which represents the center of the circular track.
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f(x) is the same as y just that we need to use it as f(x)= Instead of y=
The table below represents the function F.
x. 3 4 6 7 8
f(x). 9 17 65 129 257
The equation that represents this function is
1) F(x) = 3*
2) F(x) = 3r
3) F(x) = 2* + 1
4) F(x) = 2r +3
So the equation that represents the function F is F(x) = 2^(x-3) + 1.
None of the above equations represent the function given in the table. To find the equation, we need to look for a pattern in the outputs (f(x)) based on the inputs (x).
Starting with x=3, we see that f(x)=9. Moving to x=4, we see that f(x) increases by 8 to equal 17. Moving to x=6, we see that f(x) increases by 48 to equal 65. Each time we move to the next input value, the output increases by double the previous increase plus 1. This pattern can be written as:
f(x) = 2^(x-3) + 1
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0.416 (6 repeating) into fration
A rectangular container 6.5 ft long, 3.2 ft wide and 2 ft high is filled with sand to a depth of 1.3 ft. How much sand is in the container?
Answer:
Therefore, there are 27.04 cubic feet of sand in the container.
Step-by-step explanation:
We can start by calculating the volume of the rectangular container:
Volume = length x width x height
Volume = 6.5 ft x 3.2 ft x 2 ft
Volume = 41.6 cubic feet
Since the sand fills the container to a depth of 1.3 feet, we can calculate the volume of the sand as follows:
Volume of sand = length x width x depth of sand
Volume of sand = 6.5 ft x 3.2 ft x 1.3 ft
Volume of sand = 27.04 cubic feet
Therefore, there are 27.04 cubic feet of sand in the container.
At a toy store, a small bag contains 25 marbles, and a medium sized bag contains 7S marbles. The ratio of the number of marbles in the small bag to the number of marbles in the medium bag is equivalent to the ratio of the number of marbles in the medium bag to the number of marbles to the large bag. How many marbles are in the large bag?
Answer:
Let the number of marbles in the large bag be L. Then we have: 25 : 7S = 7S : L Multiplying both sides by 7S, we get: 25(7S) = (7S)^2 : L 175S = 49S^2 : L L = (49S^2) / 175 L = (7S^2) / 25 Therefore, the number of marbles in the large bag is (7/25) times the number of marbles in the medium bag.
Part II:
a. What is the domain of Marco's mapping diagram?
b. What is the range of Marco's mapping diagram?
Answer:
1.yes it's a function
a.1,2,3,4,5
b.40,80,120,160,200
what is the probability the proportion of total weight contributed by the fine powders exceeds one half
The approximate probability that more than 10% of the sample would report experiencing extreme levels of stress during the past month, assuming the true proportion is 15%, is 0.9693
To solve this problem, we will use the normal approximation to the binomial distribution. We can assume that the number of students who report experiencing extreme levels of stress follows a binomial distribution with parameters n = 160 and p = 0.15, where n is the sample size and p is the true proportion of students who have experienced extreme levels of stress in the population.
The expected value of the number of students who report experiencing extreme levels of stress in the sample is:
E(X) = np = 160 * 0.15 = 24
The variance of the number of students who report experiencing extreme levels of stress in the sample is
Var(X) = np(1-p) = 160 * 0.15 * 0.85 = 18.36
The standard deviation of the number of students who report experiencing extreme levels of stress in the sample is
SD(X) = sqrt(Var(X)) = sqrt(18.36) = 4.28
To calculate the probability that more than 10% of the sample would report experiencing extreme levels of stress during the past month, we need to convert the percentage into a number. Since the sample size is 160, 10% corresponds to 16 students. We want to find the probability that X > 16.
To standardize the distribution, we calculate the z-score
z = (16 - 24) / 4.28 = -1.87
Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than -1.87, which is approximately 0.0307. Therefore, the probability that more than 10% of the sample would report experiencing extreme levels of stress during the past month is approximately 1 - 0.0307 = 0.9693
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I have solved the question in general, as the given question is incomplete.
The complete question is:
Suppose that 15%, percent of the 1750 students at a school have experienced extreme levels of stress during the past month. A high school newspaper doesn't know this figure, but they are curious what it is, so they decide to ask a simple random sample of 160 students if they have experienced extreme levels of stress during the past month. Subsequently, they find that 10, percent of the sample replied “yes” to the question.Assuming the true proportion is 15, percent, what is the approximate probability that more than 10, percent of the sample would report that they experienced extreme levels of stress during the past month?
under 21
21-34
35-54
55 and
older
Total
Basketball Football Soccer Baseball
10
9
8
5
32
N
7
10
5
7
29
10
5
10
8
Sport
33
9
9
5
9
29
Other/Hate
Sports
6
10
7
6
29
Total
42
32 133
43
35
32
152
What percent of the people between the ages of 35 and 54 prefer baseball? Round
your answer to the nearest whole number percent.
The percentage of the people between the ages of 35 and 54 that prefer baseball is 17.14%.
What does a preference means?A preferences means the certain characteristics that any person wants to have in a good/service to make it preferable to him.
In the table, the total number of people between the ages of 35 and 54 is 35. Out of the 35 people, the people that prefer baseball is known to be 6.
Now, the percentage between the ages of 35 and 54 that prefer baseball will be:
= Baseball preference / Total number of people aged 35 and 54
= 6/35
= 0.17142857142
= 17.14%
Read more about preference
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Answer:
(what is your question)
Write the slope-intercept form of the equation of the line passing through the point (4, 5) and perpendicular to the line y =3/8x + 3.
Answer:
Step-by-step explanation:
Because the lines are perpendicular the slopes will be negtive
reciprocals of each other. Thus slope of 3/8 becomes -8/3.
Using point slope formula: y - y1 = m(x - x1)
Substitute the point given with the new slope and solve.
y - 5 = -8/3(x - 4)
y - 5 = -8/3x - - 32/3
y - 5 = -8/3x + 32/3
y - 5 + 5 = -8/3x + 32/3 + 5
y = -8/3x + 47/3
or
y = -8/3x + 15 2/3